The amplitude of the output of an idealized amplifier at a point in time depends only on the amplitude of the input to the amplifier at that time. A non-linearity is a deviation of the behavior of a real amplifier from the idealized amplifier.
A memory effect is a form of non-linearity where the amplitude of the output of a (non-ideal) amplifier is affected by the amplitude of the input at a plurality of prior points in time. The non-linearity caused by memory effects introduces distortion into the output of the amplifier.
Memory effects may be caused by feedback loops within the amplifier that have substantial time constants, such as Automatic Gain Control (AGC) circuits and bias circuits.